This submission is migrated from previous version of oj.uz, which used different machine for grading. This submission may have different result if resubmitted.
#include <bits/stdc++.h>
#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>
using namespace std;
using namespace __gnu_pbds;
template<typename T> using Tree = tree<T, null_type, less<T>, rb_tree_tag, tree_order_statistics_node_update>;
typedef long long int ll;
typedef long double ld;
typedef pair<int,int> pii;
typedef pair<ll,ll> pll;
#define fastio ios_base::sync_with_stdio(false); cin.tie(NULL)
#define pb push_back
#define endl '\n'
#define sz(a) (int)a.size()
#define setbits(x) __builtin_popcountll(x)
#define ff first
#define ss second
#define conts continue
#define ceil2(x,y) ((x+y-1)/(y))
#define all(a) a.begin(), a.end()
#define rall(a) a.rbegin(), a.rend()
#define yes cout << "Yes" << endl
#define no cout << "No" << endl
#define rep(i,n) for(int i = 0; i < n; ++i)
#define rep1(i,n) for(int i = 1; i <= n; ++i)
#define rev(i,s,e) for(int i = s; i >= e; --i)
#define trav(i,a) for(auto &i : a)
template<typename T>
void amin(T &a, T b) {
    a = min(a,b);
}
template<typename T>
void amax(T &a, T b) {
    a = max(a,b);
}
#ifdef LOCAL
#include "debug.h"
#else
#define debug(x) 42
#endif
/*
*/
const int MOD = 1e9 + 9;
const int N = 1e5 + 5;
const int inf1 = int(1e9) + 5;
const ll inf2 = ll(1e18) + 5;
#include "gondola.h"
int valid(int n, int a[])
{
    rep(i,n) a[i]--;
    
    set<int> st;
    rep(i,n){
        if(st.count(a[i])){
            return 0;
        }
        st.insert(a[i]);
    }
    int val = -1;
    rep(i,n){
        if(val != -1){
            val = (val+1)%n;
        }
        if(a[i] >= n) conts;
        if(val == -1){
            val = a[i];
        }
        else{
            if(a[i] != val){
                return 0;
            }
        }
    }
    return 1;
}
//----------------------
int replacement(int n, int a[], int ans[])
{
    rep(i,n) a[i]--;
    int m = *max_element(a,a+n);
    int b[n];
    rep(i,n) b[i] = a[i];
    rep(i,n){
        if(a[i] < n){
            b[a[i]] = a[i];
            int ptr = (a[i]+1)%n;
            for(int j = (i+1)%n; j != i; j = (j+1)%n){
                b[ptr] = a[j];
                ptr = (ptr+1)%n;
            }
            break;
        }
    }
    rep(i,n) a[i] = b[i];
    vector<int> pos(m+5,-1);
    rep(i,n) pos[a[i]] = i;
    rep(i,n) b[i] = i;
    set<int> st;
    rep(i,n){
        if(b[i] != a[i]){
            st.insert(i);
        }
    }
    int siz = 0;
    for(int x = n; x <= m; ++x){
        if(pos[x] != -1){
            int i = pos[x];
            assert(st.count(i));
            st.erase(i);
            ans[siz++] = b[i];
            b[i] = x;
        }
        else{
            assert(!st.empty());
            int i = *st.begin();
            ans[siz++] = b[i];
            b[i] = x;
        }
    }
    rep(i,n) assert(a[i] == b[i]);
    rep(i,siz) ans[i]++;
    return siz;
}
//----------------------
ll bexp(ll a, ll b) {
    if (a == 0) return 1;
    ll res = 1;
    while (b) {
        if (b & 1) res = res * a % MOD;
        a = a * a % MOD;
        b >>= 1;
    }
    return res;
}
int countReplacement(int n, int a[])
{
    if(!valid(n,a)){
        return 0;
    }
    int m = *max_element(a,a+n);
    int b[n];
    rep(i,n) b[i] = a[i];
    rep(i,n){
        if(a[i] < n){
            b[a[i]] = a[i];
            int ptr = (a[i]+1)%n;
            for(int j = (i+1)%n; j != i; j = (j+1)%n){
                b[ptr] = a[j];
                ptr = (ptr+1)%n;
            }
            break;
        }
    }
    rep(i,n) a[i] = b[i];
    vector<int> pos(m+5,-1);
    rep(i,n) pos[a[i]] = i;
    set<int> st;
    rep(i,n){
        if(a[i] != i){
            st.insert(i);
        }
    }
    set<int> there;
    rep(i,n){
        if(a[i] >= n){
            there.insert(a[i]);
        }
    }
    vector<int> c(all(there));
    ll ans = 1;
    if(!c.empty()){
        ans = bexp(sz(c),c[0]-n);
    }
    ll siz = sz(c);
    rep(i,sz(c)-1){
        siz--;
        ans = ans*bexp(siz,c[i+1]-c[i]-1)%MOD;
    }
    bool all_big = true;
    rep(i,n){
        if(a[i] < n){
            all_big = false;
        }
    }
    if(all_big){
        ans = ans*n%MOD;
    }
    return ans;
}
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